Asymptotic normality through factorial cumulants and partitions identities

Konstancja Bobecka-Wesołowska , Pawel Hitczenko , Fernando Lopez-Blazquez , Grzegorz Rempala , Jacek Wesołowski

Abstract

In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments, as (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for "moments" of partitions of numbers. The general limiting result is then used to (re)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution.
Author Konstancja Bobecka-Wesołowska (FMIS / DSPFM)
Konstancja Bobecka-Wesołowska,,
- Department of Stochastic Processes and Financial Mathematics
, Pawel Hitczenko
Pawel Hitczenko,,
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, Fernando Lopez-Blazquez
Fernando Lopez-Blazquez,,
-
, Grzegorz Rempala
Grzegorz Rempala,,
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, Jacek Wesołowski (FMIS / DPMS)
Jacek Wesołowski,,
- Department of Probability and Mathematical Statistics
Journal seriesarXiv:1106.4684, (0 pkt)
Issue year2011
Keywords in EnglishMathematics - Probability, Primary 60F05, Secondary 05A17, 11P84
URL http://arxiv.org/abs/1106.4684
Score (nominal)0
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